Macromolecules 1!396,28, 517-521
617
Determination of the Coupling Parameter of Local Segmental Motion in Poly(isobuty1ene) by Photon Correlation Spectroscopy A. K. Rizos* Department of Chemistry, University of Crete, Heraklion 71409, Crete, Greece, and Research Center of Crete, Heraklion 7111 0, Crete, Greece
T. Jian Research Center of Crete, P.O. Box 1527, Heraklion 71110, Crete, Greece
K. L. Ngai Naval Research Laboratory, Washington, D.C. 20375-5320 Received June 8,1994; Revised Manuscript Received October 17, 1994@
ABSTRACT: Many workers in the past have found that poly(isobuty1ene) (PIB) exhibits viscoelastic properties distinct from other commonly known amorphous polymers. PIB has perhaps the most compact and symmetric monomer chemical structure among amorphous polymers, which leads to the expectation that it has a smaller capacity for intermolecular coupling and a lower degree of cooperativity of the local segmental motion. In the framework of the coupling model this expectation for PIB implies that it has a smaller coupling parameter which is sufficient to explain its various distinct viscoelastic properties as demonstrated in previous works. Up to now there is no direct determinationof the coupling parameter for local segmental motion of PIB to confirm that it is indeed smaller compared with other amorphous polymers. Dielectric spectroscopy is inapplicable to PIB because the monomer has a negligible dipole moment. Mechanicalspectroscopic measurements performed on PIB have not yielded unambiguous results because of the difficulty of isolating the contribution of the local segmental motion from the experimental data. In this work we have resorted to photon correlation spectroscopy and successfully obtained the correlation function of the local segmental motion of PIB which can be well fit by a Kohlrausch stretched exponential function. The stretch exponent, #has I, the value of 0.56. The coupling parameter, given by 1 - ,B, has the value of 0.44 for PIB which is indeed significantlysmallercompared with other amorphous polymers and consistent with the value we deduced indirectly from other experiments.
Introduction Throughout the history of the study of viscoelastic properties of polymers poly(isobuty1ene) (PIB) has continued to show distinct and sometimes even unique behaviors not found in other polymers. As early as 1953 Fitzgerald, Grandine, and Ferry1p2 found from their complex shear compliance, J* = J’ - iJ”,measurement of PIB that it has a much broader dispersion in the glass-rubber transition region and a variation of compliance with frequency more gradual than has been found for other polymers. The distribution function of relaxation times of PIB conforms closely to the rU2 predicted by the Rouse theory3 which incidentally was proposed at approximately the same time, while in many other polymers, including polystyrene, the distribution function departs from the Rouse prediction. The frequency dependence of the loss tangent, S’IJ’, indicates the presence of a second, smaller maximum which did not appear in other Tobolsky and co-workers4p5studied extensively the viscoelastic property of a high molecular weight PIB (National Bureau of Standards sample distributed by Marvin) and found that it corresponds very well to that predicted by his wedge-box distribution model which in the glass-rubber transition zone has characteristics very similar to that predicted by the Rouse model. The fact that PIB adheres to the Rouse model prediction while many other polymers do not has led Tobolsky‘j to generalize the Rouse model by his construction of two- and threedimensional damped Debye oscillator models for other polymers. Aklonis and c o - ~ o r k e r sused ~ , ~ the index of
* Abstract published in Advance ACS Abstracts, December 15, 1994.
steepness, defined as the absolute value of the maximum slope of a logarithmic plot of the stress relaxation function of time, to distinguish PIB which has the minimum value of 0.5 from other polymers. More recently we have foundgJOthat among amorphous polymers PIB has the weakest temperature dependence of the local segmental relaxation time, t*, in a “cooperativity plot” which is a logarithmic plot of T* against T.JT. Here Tg is the operationally defined glass temperature at which t*(TJ reaches an arbitrarily chosen long time, say 100 s, which is then fured for all polymers in making the c o m p a r i s ~ n . ~AJ recent ~ creep and recoverable creep compliance measurement made on a high molecular weight entangled PIBll have found that the terminal and the local segmental relaxations of PIB have nearly the same temperature dependence, while in other high molecular weight polymers such as polystyrene the segmental relaxation time has a stronger temperature dependence than that of the terminal r e l a x a t i ~ n . ~ J l -The ’ ~ same measurements performed on a lower molecular weight, unentangled PIB sample15 show that the anomalous decrease of the steady-state recoverable compliance, Je,with decreasing temperature which had been observed previously in other polym e r ~ is~drastically ~ - ~ ~ reduced in PIB. The distinctive viscoelastic properties of PIB listed above has been rationalized or explained in the framework of the coupling model.18 These explanationsgJ0J8J9 are based on the premise that, among the better known amorphous polymers, PIB has the most symmetric and compact monomer structure which minimizes the intermolecular interactions or the degree of cooperativity between the monomers. In the coupling model the degree of intermolecular cooperativity of the local
0024-9297/95/2228-0517$09.00/00 1995 American Chemical Society
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Macromolecules, Vol. 28, No. 2, 1995
segmental (a)relaxation is specified by the coupling parameter, nu, which determines the dispersion of the relaxation through its correlation function being given by the Kohlrausch stretched exponential,
on a sample of PIB. The experimental results and the coupling parameter nu deduced from the data will be discussed in connection with the distinct viscoelastic properties of PIB.
Experimental Section The temperature dependence o f t * is also determined and is given by the relation t*
= [5,(T)1
l/(l-na)
(2)
k Samples. The polybobutylene) (PIB)samples studied in this work were purchased from Polysciences. The glass transition temperature (T,)was measured by differential scanning calorimetry with a DSC Mettler instrument at a scan rate of 10 "C/min. Gel permeation chromatographic results in THF at 30 "C on the low molecular weight sample show that it is quite polydisperse with M,, = 2530 and M , = 9800. The higher molecular weight sample has M , = 160 000 and is quite monodisperse with M,/M,, = 1.05.
where &dT) is the friction factor before the effect of intermolecular coupling on the relaxation process is considered. As have been shown in previous w o r k ~ , ~ J the ~ J ~ J ~ B. Photon Correlation Spectroscopy (PCS).The aumanifestly distinct viscoelastic properties of PIB can be tocorrelation function G,(q,t) of the polarized light scattering intensity was measured at a scattering angle of 90"at different explained quantitatively, provided that indeed PIB temperatures, where q = (4nn/1) sin(0/2)is the magnitude of among amorphous polymers has a smaller value of n u the scatteringvector at scattering angle 0 , 1 is the wavelength, as expected also by the coupling model based on a and n is the refractive index. The light source was an Ar+ comparison of the chemical structure of PIB with those laser (Spectra-Physics2020) operating at 1= 488 nm with a of other amorphous polymers. Thus a burning question power of 100 mW. The incident beam was polarized vertically is the exact value of nu or interchangeably the stretch (v) with respect to the scattering plane using a Glan polarizer. exponent, p 1 - nu, in eq 1, of PIB. Normally for The vertical (V) polarized scattered light was measured using many amorphous polymers the coupling parameter can a Glan-Thomson polarizer (Halle-Berlin). The function G,be obtained directly from the stretched exponential form ( t ) was measured with an ALV-5000 digital correlator that of the correlation function which can be deduced from covered a broad dynamic range of about 10 decades. The d i e l e ~ t r i c l ~and - ~ mechanical23 ~ measurements. First, desired correlation function g(q,t) is given by g(q,t) = [(G,PIB is not dielectrically active which rules out dielectric (q,t) - l)/fly2 where f is the instrument factor that can be measurements. Of course deliberate contamination of calculated by means of a standard. PIB will introduce electric dipoles into the polymer chain which can be used to monitor the segmental Results motion.24 The dielectric spectrum will necessarily be further broadened by inhomogeneities and randomness The measured intensity autocorrelation functions of introduced in the contamination process, rendering it the PIB sample with M , = 9800 are clearly bimodal useless to deduce the exact value of nu for PIB. Second, and, in this respect, very similar t o what has been seen the distinct character of the viscoelastic spectrum of PIB before in plasticized polydisperse poly(cyclohexy1methhaving a much broader dispersion in the glass-rubber acrylate) (PCHMA)29and PMMA.30 In all these cases transition region made it difficult if not impossible to the polarized correlation functions reveal clearly two isolate the local segmental relaxation contribution from steps or two processes. The fast process is due to mechanical relaxation or compliance measurements. 13C density fluctuations (which will later be identified with nuclear magnetic resonance (NMR) measurement is the local segmental or a relaxation), and the slow sensitive only to the local segmental motion. Applicaprocess is due to concentration fluctuations. Density tion of such a NMR technique to PIB25has enabled its and concentration fluctuations were observed together segmental dynamics to be monitored and the weak by PCS for the first time in polydisperse low molecular temperature dependence of its t* to be verified. Unweight poly(methylpheny1siloxane)(PMPS).28The simifortunately this NMR technique cannot provide a quantitative estimate of nu. larity of the PIB data to these previously published In spite of the fact that PIB plays an important and results suggests a similar interpretation of the meaunique role in the study of viscoelasticity of polymers, sured photon correlation function. It has been repeatdirect experimental data that give information of the edly found in many amorphous polymers that the stretch exponent,3! , = 1 - nu, for the local segmental correlation function of the fast process caused by local motion in PIB have so far been nonexistent. Photon segmental motion is well represented by the Kohlrausch correlation spectroscopy (PCS) has proven to be useful stretched exponential Also theoretically to characterize the local segmental dynamics of amorthe coupling model has suggested the correlation funcphous polymers near and above Tg.17,21,26-30 The techtion of local segmental motion should have the stretched nique requires a sample of good optical quality, and thus exponential form. We follow this empirically estabit is not immediately applicable to any amorphous lished fact and theoretical suggestion in using the polymer. Fortunately this is not the case for PIB. stretched exponential function to represent the correlaP a t t e r ~ o n ~has ~ ,demonstrated ~~,~~ that one can obtain tion function of the fast process. There is no theoretical Brillouin scattering data a t high frequency on PIB. guidance to what the correlation of the slow process However, as far as we know, PCS has remained unexshould be. Experimentally the correlation function of plored as an option to determine the correlation function the slow process has been observed to be slightly of segmental motion in PIB. This state of affair is broader than an exponential function and can be fit by probably due to the fact that it is relatively dificult to a stretched exponential, with the stretch exponent obtain dynamic light scattering data of PIB near and Thus we represent the having a value close to above Tg and the concern of possible complications measured correlation function of the two well-separated caused by the slight tendency of PIB to crystallize. In processes at temperatures above Tg by the sum of two this paper we report PCS measurements performed l.17728-30
Coupling Parameter of Local Segmental Motion in PIB 519
Macromolecules, Vol. 28, No. 2, 1995
'
0._..._...... 0 222K
- D-.-.-.fl 229 K
' O0.08 JO
?--3 s
Figure 1. Measured correlation function for the 9800 molecular weight PIB at 222 and 229 K. The corresponding retardation time spectra, L(1og t),obtained by inverse Laplace transform are also shown as a function of log t in the inset.
t
.
,
PIE (M,=8900), T=222 K
-4
1
-2
log(t/s)
Figure 2. Correlation function of the local segmental motion obtained by subtracting the slow process from the experimental data. Shown also is the Kohlrausch stretched exponential fit to the data with ,&= 0.56. The quality of the fit is indicated by the percentage of deviation (lower part).
KWW functions:
where af,a,,zf, and zs and the p's are treated as adjustable parameters. Figure 1shows the correlation function for the lower molecular weight PIB a t 222 and 229 K. The KWW fit to the experimental spectra gave ,& = 0.59 f 0.05. The fast-decaying portion of the bimodal correlation function, identified with density fluctuation, was obtained by subtraction of the slow component. This was accomplished by first making an inverse Laplace transform (ILT) analysis33 and subsequently deleting the contributions from the slow process in the data file. The residual correlation function was then analyzed using a single KWW fit to obtain the relaxation time and the stretch exponent of the fast process. The inset of Figure 1 shows the retardation spectrum, L(ln t),has two peaks corresponding to the two processes a t two temperatures. The temperature shift factors of the most probable retardation times of the two processes as defined by the positions of the peaks of the L's are not the same. The fast process (which we shall identify with the local segmental motion
-4
-2
0
2
4
log(t/s)
Figure 3. Result of the inverse Laplace transform (lowerpart) of the measured correlation function (upper part) of the 9800 molecular weight PIB at 222 K.
below) has a slightly larger shift factor. This moderate breakdown of thermorheological simplicity is consistent with what has been seen before by creep compliance measurements in another sample of PIB with M, = 10 700.15 The degree of thermorheological complexity found in PIB is considerably less than that exhibited by PMPS,28 and PMMA30 in similar experiments and by polystyrene in a different e ~ p e r i m e n t . ' ~ , ~ ~ ~ ~ ~ In order to present that part of the correlation function due to the segmental relaxation in a clear manner, we show in Figure 2 the residual correlation function obtained after subtraction of the slow process. The full line is the single KWW fit with pf = 0.56 f 0.08. The shape parameter or the stretch exponent, p,, for the slow process is close to 1. The separation in time scales of the fast and slow processes measured by the difference between log(@) and log(t,*) is about 5-6 decades (see also the separation of the peaks of the retardation spectrum in Figure 3, upper part). This separation is almost the same as the width of the glassrubber transition zone of a nearly monodisperse PIB sample 1-7 which has molecular weight M, = 10 70015 comparable to that of our present low molecular weight sample. The width of the glass-rubber transition zone can be readily obtained from the plot of log(J,(t)) against log t, where J,(t) is the recoverable creep compliance (see Figure 2 of 15). Such a good correspondence between the difference, log(z,*) - log(tf*), from our PCS measurement and the width of the glass-rubber transition zone from creep compliance measurement supports the identification of the fast process as density fluctuation caused by the local segmental motion and the slow process as concentration fluctuation caused by the Rouse diffusional mode in our low molecular weight PIB sample. Moreover, the recoverable compliance data of PIB 1-7 published in ref 15 have enabled us to determine approximately the retardation time of local segmental motion. We find at T = 222.9 K the retardation time of s which is nearly the same PIB 1-7is approximately as the retardation time at the position of the peak of L obtained from the PCS data of our 9800 molecular weight sample at 222 K. This comparison of the local segmental retardation times obtained by PCS with that determined by another technique on samples with similar molecular weights helps to confirm the identification of the fast process with the local segmental motion in PIB.
520 Rizos et al.
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A similar interpretation has been given for the dynamic light scattering data of PMPS,I7 plasticized PCHMA,29 and PMMAS3O Creep compliance data of PMPS and PMMA are'available from Plazek and co~ o r k e r s l and ~ t ~can ~ be used to estimate the difference of the time scales of the fast (local segmental) process and the slow (the end of the glass-rubber softening dispersion indicated by the position of the first peak of the retardation spectrum12J3) process. Like in the present case of PIB, there is also good correspondence between the estimate of the separation between the two processes from compliance data and dynamic light scattering data in PMPS and PMMA. On comparing the separation in time scales of the fast and slow processes of PIB seen by dynamic light scattering with that of other polymers,17,29,30,35 we can attest to the known fact that PIB has a much broader glass-rubber transition zone than other amorphous p o l y m e r s . ' ~ ~ , ~ , ~ An alternative approach t o eq 3 is to express g(t) in terms of a continuous distribution of relaxation times, by making use of the inverse Laplace transform of the time-correlation function using the CONTIN algorithm:33
PIB (MW=160000),222 K 0.050
I
I
I
I
I
I
I
I
I
(4) with L(ln z) being the distribution of retardation times. Figure 3 shows an experimental correlation function taken at 222 K together with the result of the CONTIN analysis. A two-peak structure is clearly evident in the short time portion, -6 < log(z/s) < 0, of the correlator time window. Guided by the creep compliance datal5 in the manner as discussed before, the faster and more prominent peak is identified with the local segmental relaxation. The broad shoulder on the short time side seems to indicate the presence of secondary/?-relaxation as well, although the quality of the data is not good enough for us to make a definitive statement at this time. The other peak of the pair located a t about 2 decades longer may correspond to motions (sub-Rouse modes) that involve a length scale intermediate between that of the local segmental motion and the Gaussian submoleculefor Rouse modes. The slow process located nearly at the long time limit of the correlator window exhibits a sharp peak which naturally is contributed by the diffusional mode that gives rise to concentration fluctuation in the low molecular weight polydisperse sample. Figure 4 displays a typical autocorrelation function for the higher M , and nearly monodisperse PIB sample a t 222 K. In this sample the slow process of concentration fluctuation is not seen. The reason for its absence is a combination of near monodispersity which suppresses concentration fluctuation and high molecular weight which shifts the time scale of the slow process beyond the correlator time window. The KWW fit to the experimental spectrum gave /?f = 0.55 f 0.08 which is close to the value determined in the lower molecular weight sample. The intensity of the scattered light remains constant as a function of time as shown by the inset of Figure 4,which indicates that crystallization is not a concern over the temperature range of the present investigation. However, below -60 "C the scattered light intensity increased rapidly with time, indicating the onset of crystallization. The high and low molecular weight data at 222 K are compared in Figure 5. The retardation spectrum of the fast process of 9800 PIB is very similar in shape to that of the 160 000 PIB. The similarity of the shape of L
-
-
V - - - .D PIB(160000) (3
1
I
I
I
I
I
I
I
I
I
2r----i1
Y
I
I
I
-
0.08 j - L
0 PIB(9800)
0.15
0.10
0.05
0 -6
-4
-2
0
2
Figure 6. Comparison of the measured correlation functions and calculated retardation spectra of the two samples of PIB. indicates that the stretched exponent /?f is about the same for the two samples, which reaffirms the interpretation of the fast process as due t o local segmental motion. This is because for local segmental motion its stretch exponent is independent of the molecular weight and polydispersity of the sample. The most probable retardation times defined by the positions of the peaks of L of the two samples differ by approximately 2 decades, with that of the low molecular weight PIB being naturally shorter.
Discussion PIB occupies a unique position among amorphous polymers in the development of the field of viscoelasticity of polymers. As enumerated in the Introduction, there are several viscoelastic properties found in PIB which are not shared by other commonly known amorphous polymers. The important question of why PIB has such unique properties has been addressed in the literature by many authors.2-8 An explanation of the distinct viscoelastic manifestation of PIB2-11J5 is certainly very desirable. A different angle of approach to viscoelasticity has been introduced by the coupling
Macromolecules, Vol. 28,No. 2, 1995
model,18which emphasizes the importance of the inclusion in the consideration of dynamic constraints or “cooperativity” between molecular moieties when describing their motions in dense-packed systems. We still have to first consider the mobility or the friction factor, Co(T), which governs initially at sufficiently short times the independent relaxation rate, z0-l = Co(T), of motion of molecules. Co(T) is determined by some static “mean-field”consideration of the dense-packed systems which may very well be approximated by free volume2 or configurational entropy36considerations. However, once the molecular moieties are set in motion and the corresponding relaxation process is underway, the dynamic constraints or many-body correlations after a time, t,, characteristic of the molecular interaction Hamiltonian will take over to determine ultimately the effective relaxation rate. Based on theoretical conside r a t i o n ~ the , ~ ~coupling ~ ~ ~ model proposes that t, is temperature insensitive and the effect of the dynamic constraints can be represented as a rate slowing down to give rise to the stretched exponential given by eq 1, with the effective relaxation time, z*, given in terms of the independent relaxation time to and crossover time t, by the second relation:
Coupling Parameter of Local Segmental Motion in PIB 621
References and Notes
(1)Fitzgerald, E. R.; Grandine, L. D.; Ferry, J. D. J . Appl. Phys. 1953,24,650. Ferry, J. D.; Grandine, L. D.; Fitzgerald, E. R. J . Appl. Phys. 1953,24,1953. (2)Ferry, J. D. Viscoelastic Properties of Polymers, 3rd ed.; John Wiley and Sons: New York, 1980. (3)Rouse, P. J . Chem. Phys. 1953,21,1272. (4)Catsiff, E.; Tobolsky, A. V. J . Colloid Sci. 1955,10,375. (5)Tobolsky, A.V.Properties and Structure of Polymers; Wiley: New York, 1960. Tobolsky, A. V. J . Appl. Phys. 1956,27, 673. (6)Tobolsky, A. V. J . Chem. Phys. 1962,37,1575. Tobolsky, A. V.; DuPre, D. B. Adu. Polym. Sci. 1969,6,103. (7) Aklonis, J. J. Ph.D. Thesis, Princeton University, Princeton, NJ, 1965. Aklonis, J. J.; Rele, V. B. J . Polym. Sci. 1974,C46, 127. (8) Aklonis, J. J.; MacKnight, W. J.; Shen, M. Introduction to Polymer Viscoelasticity; Wiley: New York, 1972. (9)Plazek, D. J.; Ngai, K. L. Macromolecules 1991,24, 1222. (10)Bohmer, R.;Ngai, K. L.; Angell, C. A.; Plazek, D. J. J . Chem. Phys. 1993,99,4201. (11)Plazek, D. J.; Zheng, X. D.; Ngai, K. L. Macromolecules 1992, 25,4920. (12)Plazek, D. J. J . Polym. Sci., Polym. Phys. Ed. 1982,20,729. (13)Plazek, D. J. Polym. J . 1980,12,43. (14)Ngai, K. L.; Plazek, D. J. J . Polym. Sci., Part B: Polym. Phys. 1986,24,619. (15)Ngai, K.L.;Plazek, D. J.; Bero, C. A. Macromolecules 1993, 26, 1065. (16)Plazek, D. J.; ORourke, V. M. J . Polym. Sci., Polym. Phys. Ed. 1971,9,209. Recently a quasielastic neutron scattering experiment39 (17)Plazek, D. J.; Bero, C.; Neumeister, S.; Floudas, G.; Fytas, has given direct confirmation of these principal results. G.; Ngai, K. L. Colloid Polym. Sci. 1994,272,1430. (18)For a recent review, see: Ngai, K. L. In Effect of Disorder Such a simple relation given by eq 5 has led to many in Relaxation Processes; Richert, R., Blumen, A., Eds.; predictions which have been verified by applications to Springer-Verlag: Berlin, 1994;p 89. experiments.18 Examples related t o PIB can be found (19)Ngai, K.L.;Roland, C. M. Macromolecules 1994,26, 6824. in refs 11 and 15. (20)Boesse, D.; Kremer, F. Macromolecules 1990,23,829. Applying to local segmental motion, the coupling (21)Boesse, D.; Momper, B.; Meier, G.; Kremer, F.; Hagenau, J.model expects a chemical structural dependence of the U.; Fischer, E. W. Macromolecules 1989,22,4416. coupling parameter, nu. Intuitively as well as theoreti(22)Schlosser, E.; Schonhals, A. Colloid Polym. Sci. 1989,267, 963. cally from the dependence of nu on the interaction (23)Roland, C. M.; Ngai, K. L. Macromolecules 1991,24, 5315; H a m i l t ~ n i a n , ~PIB ’ ~ ~having ~ the most symmetric and 1992,25,7031. compact monomer structure among amorphous poly(24)Kabin, S.P.; Mikhailov, G. P. Zh. Tekhn. Fiz. 1956,26,511. mers is expected to have a smaller nu compared with (25)McGrath, K.;Ngai, K. L.; Roland, C. M. Macromolecules 1992, that of other vinyl polymers such as polystyrene which 25,4911. has nu = 0.65. A n indirect determination of an ap(26)Patterson, G. D. In Dynamic Light Scattering; Pecora, R., Ed.; proximate value of na = 0.4 for PIB was made possible John Wiley: New York, Chapter 6,p 260. (27)Patterson, G. D.; Linsey, C. P.; Stevens, J. R. J . Chem. Phys. by comparing the measured momentum transfer, Q, 1979,70,643. dependence of the segmental relaxation times obtained (28)F’ytas, G.; Dorfmuller, Th.; Chu, B. J . Polym. Sci., Polym. by quasielastic neutron scattering with the coupling Phys. Ed. 1984,22,1471. Ngai, K. L.; Fytas, G. J . Polym. model predicted dependence of Q2/(1-Q.18940Another Sci., Part B: Polym. Phys. 1986,24,1683. indirect determination of nu can be obtained 6.om the (29)Fytas, G.;Floudas, G.; Ngai, K. L. Macromolecules 1990,23, empirically found correlation between the temperature 1104. sensitivity, S = d log(z*)/d(TJT) determined at Tgwhich (30) Floudas, G.; Rizos, A.; Brown, W.; Ngai, K. L. Macromolecules 1994,27,2719. is operationally defined as the temperature as which (31)Patterson, G. D. J . Polym. Sci., Polym. Phys. Ed. 1977,15, z*(T,) = 100 s, with n,.9J0 An extrapolation of this 455. correlation between S and na defined by other amor(32)Patterson, G. D. J. Chem. Phys. 1984,81,1666. phous polymers t o PIB (see Figure 2 of ref 9) suggests (33)Provencer, S. W. Comput. Phys. Commun. 1982,27,213. its coupling parameter has a value of na = 0.45. These (34)See Figure 9 of: Plazek, D. J. J . Polym. Sci., Polym. Phys. two estimates of n a we deduced indirectly from other Ed. 1968,6,621. experimental data are consistent with its value that we (35)Plazek, D. J.; Tan, V.; O’Rourke, V. M. Rheol. Acta 1974,13, 367. now obtain directly by photon correlation spectroscopy. (36) Adam, G.; Gibbs, J. H. J . Chem. Phys. 1965,43,139. This value of nu is indeed smaller than other commonly (37)Ngai, K.L.; Peng, S . L.; Tsang, K. Y. Physica 1991,A191, known amorphous polymers and can explain quantita523. tively some of the differences in viscoelastic properties (38) Tsang, K.Y.; Ngai, K. L. Phys. Rev. E , submitted. between PIB and other amorphous p o l y m e r ~ . ~ JIn ~J~,~~ (39)Colmenero, J.; Arbe, A.; AlBgria, A. Phys. Rev. Lett. 1993, the future we shall further exploit the information 71,2603. obtained in this work on the local segmental motion of (40)Ngai, K. L.;Colmenero, J.; Arbe, A. Macromolecules 1993, PIB to explain other distinct viscoelastic properties of 25, 6727 Colmenero, J.; Arbe, A.; Alegria, A.; Ngai, K. L. J . Non-Cryst. Solids 1994,172-174,229. PIB. (41)Ngai, K.L.; Plazek, 4. J. In Handbook of Polymer Properties; Mark, J., Ed.; American Institute of Physics, submitted. Acknowledgment. K.L.N. is supported in part by
ONR Contract N0001494WX23010.
hfA941076G
